Yes you can file Head of Household if you didn't live together and you have a qualifying child.
Can a married person file Head of Household?
https://ttlc.intuit.com/community/married/help/can-a-married-person-claim-head-of-household-filing-s...
Here's a FAQ for Head of Household
https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/00/25539
Even though you don't live together you could still file a Joint return together. But you probably don't want to do that. No he doesn't get any info from your return. He should be filing MFS also. And you both need to file the same way. If one person Itemizes Deductions the other one must also Itemize. Or both take the Standard Deduction. And if you are in a community property state you do have to enter half of your spouse's income on your return and it tricky to figure out.
